In classical sampling theory, the signals to be sampled come from a single space. Practically, signals for sampling should be considered from the union of subspaces. This approach has applications in sparse signal representation, compressed sampling, nonuniform splines, and more. The extension of the sampling problem to a union of subspaces was introduced by Lu and Do [1]} and extended further by M. Anastasio and Cabrelli [2]}. In our setup, we are going to take a union of finitely generated multiplication invariant subspaces of \(L^2(X;\mathcal {H})\)  and discuss the injectivity of sampling operator \(T\)  on the union.
